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Quantum scattering - 1/r^2

  1. Dec 7, 2008 #1
    1. The problem statement, all variables and given/known data

    Use partial waves method to calculate scattering amplitude for a quantum particle scattering off the potential V(r) = a/r^2.

    2. Relevant equations

    3. The attempt at a solution

    To calculate phase shifts [tex]\delta_{l}[/tex] for each angular momentum's value l, it's necessary to solve Schrodnger's equation for the specified potential - but I'm unable to do it. I know that solution for a free particle can be expressed in terms of Bessel spherical functions, but in radial Schrodinger's equation we have the centrifugal term of the form l(l+1)/r^2, where l is an integer, not for arbitary potential a/r^2. Any hints?
  2. jcsd
  3. Dec 7, 2008 #2


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    The radial equation doesn't care whether or not l is an integer ...
  4. Dec 7, 2008 #3
    Ok, but in the noninteger case the solutions are special functions, from which I don\t know how to calculate the phase factors in question.
  5. Dec 7, 2008 #4


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    Science Advisor

    The asymptotic properties of Bessel functions hold whether or not the index is an integer.
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